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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic behaviour
of Castelnuovo-Mumford regularity


Author: Vijay Kodiyalam
Journal: Proc. Amer. Math. Soc. 128 (2000), 407-411
MSC (1991): Primary 13D02; Secondary 13D40
Published electronically: July 6, 1999
MathSciNet review: 1621961
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Abstract: Let $S$ be a polynomial ring over a field. For a graded $S$-module generated in degree at most $P$, the Castelnuovo-Mumford regularity of each of (i) its $n^{\operatorname{th}}$ symmetric power, (ii) its $n^{\operatorname{th}}$ torsion-free symmetric power and (iii) the integral closure of its $n^{\operatorname{th}}$ torsion-free symmetric power is bounded above by a linear function in $n$ with leading coefficient at most $P$. For a graded ideal $I$ of $S$, the regularity of $I^{n}$ is given by a linear function of $n$ for all sufficiently large $n$. The leading coefficient of this function is identified.


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Additional Information

Vijay Kodiyalam
Affiliation: The Institute of Mathematical Sciences, Chennai, India 600113
Email: vijay@imsc.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05020-0
PII: S 0002-9939(99)05020-0
Received by editor(s): October 28, 1997
Received by editor(s) in revised form: April 15, 1998
Published electronically: July 6, 1999
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society